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@nickgreenberg Regarding your #4, I think I have a solution, at least for 2 trigger inputs. You're going to need two sequential switches.

The second one will be your gate generator. Wire the out to wherever you need it to go, leave the first input disconnected, and send a constant +5v into the second one. The trigger in will be the output of the other switch. Initially the gate is low, when the trigger arrives it goes high, the next trigger makes it low again, and so on.

The first one will do the switching logic. Put you two trigger channels into the two inputs, A and B. The output will be multed, once to trigger the other switch, and once to the trigger of this switch. Initially the switch passes input A to the output, and input B is ignored. When a trigger arrives on A the gate is turned on by the second switch, and the first switch also advances so it is now listening to trigger B. Now when a trigger arrives on B all the same stuff happens in reverse.

I'm sure there are better ways to do this, but this ought to work. (I'm not really clear what you had in mind for the third trigger but you may be able to adapt this scheme.)

OTOH if your triggers were gates instead you could probably do the job with some Boolean logic.